It is a construct. One can argue that G / general intelligence factor does not exist, I believe it does since mental ability seems to correlate with general competence across many domains. I believe it's a better argument that IQ tests may not be an effective method of deriving it.
The g factor (also known as general intelligence, general mental ability or general intelligence factor) is a construct developed in psychometric investigations of cognitive abilities and human intelligence. It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the fact that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks. https://en.wikipedia.org/wiki/G_factor_(psychometrics)